texture mapping without distortion
You probably distort UVs by image shape. This is why your texture is distorted diagonally from left top to right bottom corner. 

Use some 2D editor to fix texture perspective and use rectangular shape for UVs to mach shape of plane. Never distort UVs. In best case, they should have exact the same shape as faces in 3D object.

EDIT: "never" is too strong expression, sometimes is helpful or
 necessary, but definitely not in your case.